1. Field of the Invention
The present invention relates to a frequency demodulator designed to avoid the occurrence of a reversal phenomenon in which a demodulated output from a digital FM demodulating means for a frequency modulated luminance signal reproduced in a video tape recording and/or reproducing apparatus (which apparatus is hereinafter referred to as a video tape player) is reversed.
2. Description of the Prior Art
FIG. 1 of the accompanying drawings illustrates a circuit block diagram of the prior art analog luminance signal processing circuit in the video tape player. Referring to FIG. 1, reference numeral 41 represents a transducer head amplifier for amplifying an analog reproduced FM signal picked up by a magnetic transducer head 40 from a length of magnetic tape 39. The amplified FM signal emerging from the transducer head amplifier 41 is supplied to a reproduced RF equalizer 42. The RF equalizer 42 is connected with a double limiter 43 operable to avoid any possible reversal phenomenon of the analog reproduced FM signal, supplied from the reproduced RF equalizer 42, and also to limit the same analog reproduced FM signal, which limiter 43 is in turn connected with an analog FM demodulator 44 operable to demodulate the output from the double limiter 43. The output from the analog FM demodulator 44 is in turn supplied to low pass filter 46 through a main de-emphasis circuit 45 for de-emphasizing the output from the demodulator 44.
The prior art reproduced luminance signal processing circuit of the above described construction operates in the following manner.
The analog reproduced FM signal outputted from the magnetic transducer head 40 is, after having been amplified by the transducer head amplifier 41, passed to the reproduced RF equalizer 42 having a certain operating characteristic at which the analog reproduced FM signal is modified for the purpose of avoiding the reversal phenomenon and also of securing a certain signal-to-noise ratio so that the upper and lower side-bands of the analog reproduced FM signal can occupy certain respective proportions relative to the carrier wave.
The output from the reproduced RF equalizer 42 is then supplied to the double limiter 43 which subsequently provides an output signal in the form of an analog FM signal of uniform amplitude whose reversal phenomenon is prevented. This analog FM signal emerging from the double limiter 43 is in turn demodulated by the analog FM demodulator 44. The demodulated FM signal from the analog FM demodulator 44 is supplied to the main de-emphasis circuit 45 to pass through a filter having an operating characteristic reverse to that of a pre-emphasis circuit during the recording mode and is thereafter passed through the low pass filter 46 for the removal of unwanted components therefrom.
In the prior art reproduced luminance signal processing circuit of the above described construction, where the FM wave inputted to the analog FM demodulator 44 is an unbalanced FM wave wherein, as a result of its passage through an FM transmission system of certain operating characteristic including a reproduced RF equalizer, the upper and lower side-bands are suppressed and emphasized, respectively, or emphasized and suppressed, respectively, such as observed in the FM wave appearing in the reproduced luminance signal processing circuit employed in video tape players for home use, it has been observed, and so is ascertained through a series of experiments, that the demodulated signal thereof tends to jump out of a predetermined level range to a black or white level side. When such modulated signal is de-emphasized with no correction made thereon and is outputted as a video signal, black or white short sweep lines appear on the display screen thereby to render the reproduced picture uncomfortable to look. Such a phenomenon is generally referred to as the reversal phenomenon.
FIG. 2 illustrates a circuit block diagram showing the TAN type digital FM demodulator disclosed during the session of the nationwide meeting held by the Electronic Communication Society of Japan in 1983 and, also, in IEEE Transactions on Consumer Electronics, Vol. CE. 32, No. 3, August 1986. This digital FM demodulator can be used in place of the analog FM demodulator 44 shown in FIG. 1 for the demodulation of the FM wave. Even though the digital FM demodulator is used in the manner described above, the occurrence of the reversal phenomenon cannot be eliminated.
Hereinafter, the structure and the operation of the digital FM demodulator will be discussed and, in the course thereof, the reversal phenomenon occurring in the digital FM demodulator will also be discussed.
Referring to FIG. 2, reference numeral 1 represents an analog-to-digital converter having a sampling cycle T and operable to convert the input analog FM signal into a digital signal. The FM signal so digiytized by the analog-to-digital converter 1 is shifted 90.degree. in phase by a 90.degree. phase shifter 3 to provide a signal Y. On the other hand, the output from the analog-to-digital converter 1 is also supplied to a delay compensator 2 operable to delay the digital FM signal for a predetermined length of time required for the digital FM signal to match in phase with the 90.degree. phase shifted FM signal, that is, the signal Y. Accordingly, the delayed FM signal X from the delay compensator 2 and the signal Y from the 90.degree. phase shifter 3 can be regarded as signals quantified at the same timing.
Reference numeral 4 represents a calculating circuit capable of performing a calculation of tan.sup.-1 (X/Y) with respect to the signals X and Y inputted thereto. An output from the calculating circuit 4 is supplied to a delay circuit 5 for delaying the input signal for a length of time equal to the sampling cycle T. The delayed output from the delay circuit 5 is in turn supplied to a subtractor 6 operable to subtract the output of the delay circuit 5 from the output of the calculating circuit 4.
The FM demodulating operation is carried out accordaing to the following calculations.
Assuming that the analog FM signal at a particular timing t is expressed by X(t) and the same analog FM signal which has been shifted 90.degree. in phase is expressed by Y(t), it is well known to those skilled in the art that the frequency-demodulated signal F(t) of the signal X(t) can be expressed by the following equation. EQU F(t)=(d/dt).multidot.tan.sup.-1 [X(t)/Y(t)] (1)
The term, tan.sup.-1 [X(t)/Y(t)], in the above equation (1) represents the phase of the FM wave at the timing t and, if this term is expressed by .phi.(t), the equation (1) above can be rewritten as follows. EQU F(t)=(d/dt).multidot..phi.(t) (2)
The digital FM demodulator 50 shown in FIG. 2 is a hardware which accomplishes the above discussed digital signal processing. In this digital FM demodulator 50, the calculator 4 used therein is constituted by, for example, a read-only memory whose input addresses are represented by the signals X and Y, which read-only memory is so constructed as to store, as its contents, arc tangent (tan.sup.-1) values appropriate to (X/Y). With this construction, the calculating circuit 4 can provide, as an output, a signal representative of tan.sup.-1 (X/Y) in response to the delayed and phase-shifted digital FM signals X and Y supplied thereto from the delay compensator 2 and the phase shifter 3, respectively.
The output from the calculating circuit 4 is descriptive of the phase .phi.(K.multidot.T) of the frequency modulated wave at the time t=K.multidot.T as hereinbefore described. However, if for the purpose of simplification the phase .phi.(K.multidot.T) is expressed by .phi.(K). (Hereinafter, a similar nomenclature is employed to the phases other than .phi.(K).), the output from the delay circuit 5 is expressed by .phi.(K-1) and the output from the subtractor 6 is expressed by .phi.(K)-.phi.(K-1) which is a value descriptive of the increment of the phase of the frequency modulated wave during the sampling cycle T. This difference is expressed by .DELTA..phi.(K).
The equation (2) above can be approximately expressed as follows when the sampling cycle T is sufficiently short. EQU F(K).apprxeq.[.DELTA..phi.(K)]/T (3)
Since the sampling cycle T is fixed, the output .DELTA..phi.(K) from the subtractor 6 can be similar to the demodulated signal F(K) and, therefore, the output .DELTA..phi.(K) from the subtractor 6 can be regarded as the demodulated signal.
However, the arc tangent (tan.sup.-1) is a cyclic function and the cycle thereof is 2.pi. with due regard paid to the sign taken by each of the delayed and phase-shifted digital FM signals X and Y. Assuming that a table in the read-only memory comprising the calculating circuit 4 has values ranging from zero to 2.pi., and also assuming, for example, that the value of tan-1(X/Y) of the input signals X and Y at the timing (K-1) and that at the subsequent timing (K) are 1.9.pi. (radian) and 2.1.pi. (radian), respectively, the outputs .phi.(K-1) and .phi.(K) produced successively from the calculating circuit 4 are 1.9.pi. (radian) and 0.1.pi. (radian), respectively, and therefore, a problem tends to occur in that the output .DELTA..phi.(K) [=.phi.(K)-.phi.(K-1)] from the subtractor 6 may take a negative value (-1.8.pi.), thereby inviting a discontinuity in this output.
In view of the foregoing, a discontinuity corrector 7 is employed for performing a correction in such a way that, only when the output from the subtractor 6 takes a negative value, 2.pi. is added to the negative output from the subtractor 6. With this discontinuity corrector 7 used, whenever the output from the subtractor 6 takes a negative value, the discontinuity corrector 7 can provide properly corrected outputs of the subtractor 6 with no discontinuity accompanied. The output from the discontinuity corrector 7 is hereinafter expressed by So(K). When the output So(K) from the discontinuity corrector 7 is subsequently converted by a digital-to-analog converter 9, the frequency demodulated analog signal, that is, the input signal whose frequency has been demodulated, can be obtained.
Where the FM wave inputted to the analog-to-digital converter 1 is an unbalanced FM wave wherein, as a result of its passage through an FM transmission system of certain operating characteristic including a reproduced RF equalizer, one of the upper and lower side-bands is suppressed and the other of the upper and lower side-bands is emphasized such as observed in the FM wave appearing in the reproduced luminance signal processing circuit employed in video tape players for home use, it has been observed, and so is ascertained through a series of experiments, that, in the case of the prior art digital FM demodulator shown in FIG. 2, the demodulated signal thereof tends to jump out of a predetermined level range to a black or white level side. When such demodulated signal is, with no correction made thereon, converted into the analog signal and is then outputted as a video signal, black or white short sweep lines appear on the display screen thereby to render the reproduced picture uncomfortable to look. Such a phenomenon corresponds to what is generally referred to as the reversal phenomenon occurring when the prior art analog FM demodulator is employed and, therefore, the appearance of the black or white short sweep lines on the display screen ocurring when the prior art digital FM demodulator is used is also called the reversal phenomenon for the sake of brevity.
The reversal phenomenon occurring as the result of the use of the prior art digital FM demodulator will now be discussed.
Since the carrier wave having an amplitude A and an angular frequency .OMEGA.c can be expressed on a complex plane as a vector, such vector is expressed by the following equation and is referred to as "carrier wave vector". EQU Ec(.omega.ct)=A.multidot.e.sup.j.omega.ct
Also, since when the modulated signal is expressed by em(t)=.OMEGA.d.multidot.cos .omega.mt the frequency modulated wave can be expressed by a vector having at a timing t a magnitude A and a phase expressed by (.omega.ct+.intg..sub.0.sup.t em(t)dt) in phase, this vector is referred to as "FM vector".
The FM vector, designated by E(t), can be expressed by the following equation. EQU E(t)=Ec[.omega.ct+.intg..sub.0.sup.t em(t)dt]=A.multidot.e.sup.j [.omega.ct+.intg..sub.0.sup.t em(t)dt]=Ec(.omega.ct)e.sup.jm.multidot.sin .omega.mt
wherein m represents a modulation index and is expressed by .OMEGA.d/.omega.m.
The carrier wave vector Ec(.omega.ct) rotates counterclockwise on a stationary complex plane with passage of time t while depicting a circle having a radius A. Considering the complex plane which rotates together with the carrier wave vector Ec(.omega.ct), the complex plane can be contemplated so that the carrier wave vector Ec(.omega.ct) can be always matched with a positive direction of a real axis on this complex plane.
If the complex plane is so contemplated, the tip of the frequency modulated vector E(t) depicts a trajectory of a complex number e.sup.jm.multidot.sin .omega.mt, that is, depicts an arc having the center of curvature thereof lying in alignment with the point of origin. This is referred to as a "vector trajectory" of the frequency modulated wave. In other words, the trajectory of the frequency modulated vector E(t), when the carrier wave vector Ec(.omega.ct) is taken as a reference vector, corresponds to the figure depicted on an x-y (two dimensional) plane by the frequency modulated vector E(t)=Ec(.omega.ct).multidot.[x+jy] at a timing (x, y). This is illustrated in FIG. 3.
Referring now to FIG. 3, the arch shown therein represents the trajectory of the frequency modulated vector E(t) which swings from P to Q and back to P and subsequently from P to R and back to P, that is, P.fwdarw.Q.fwdarw.P.fwdarw.R.fwdarw.P. Also, the frequency modulated vector E(t) can be expressed as follows using Bessel's function Jn(m). ##EQU1## However, if in a certain transmission system the n-th order side-band is multiplied by yn, the frequency modulated vector E1(t) obtained after having passed through such certain transmission system can be expressed as follows. ##EQU2## Therefore, the vector trajectory G(t) can be expressed as follows. ##EQU3##
Assuming, for example, that the frequency modulated wave is the one wherein the upper side-band is suppressed and the lower side-band is emphasized, the vector trajectory G(t) will depicts the shape of a ring as shown in FIG. 4 and revolves in a clockwise direction as shown by the arrows. Also, in the case of the transmission system wherein the upper side-band of the frequency modulated wave is further suppressed while the lower side-band thereof is further emphasized, the ring representing the vector trajectory G(t) expands radially outwardly and will, when noises are induced in the frequency modulated wave, depict such a trajectory containing the point of origin as shown in FIG. 5.
In view of the fact that the waveform of each of these frequency modulated waves which have been demodulated is given by the instananeous angular frequency of the vector trajectory of the frequency modulated wave, the demodulated waveform in the case of the vector trajectory as shown in FIG. 3 will represent a sine wave as shown in FIG. 6, and the demodulated waveform in the case of the vector trajectory as shown in FIG. 4 will exhibit a large positive value at a position corresponding to a point P2 shown in FIG. 7 because the point P2 approaches the point of origin with increase in instantaneous angular frequency.
Also, the demodulated waveform in the case of the vector trajectory shown in FIG. 5 will exhibit a negative value wherein the absolute value of the instantaneous angular frequency is of a very high value because it encompasses the point of origin with the point P2 located close to the point of origin, and therefore, at a position corresponding to the point P2, the demodulated wave will exhibit a negative value wherein the absolute value is of a very large value, so far from exhibiting a positive value which it ought to have taken, as shown in FIG. 8. This is called the reversal phenomenon in which the demodulated signal jumps towards the black level side.
Conversely, where the frequency modulated wave is the one wherein the lower side-band thereof is suppressed while the upper side-band thereof is emphasized, the vector trajectory G(t) depicts the shape of a ring as shown in FIG. 9 and revolves in a counterclockwise direction as shown by the arrows in FIG. 9. On the other hand, in the case of the transmission system wherein the lower side-band of the frequency modulated wave is further suppressed while the upper side-band thereof is further emphasized, the ring representing the vector trajectory will expand generally radially outwardly and will, when noises are induced in the frequency modulated wave, exhibit such a trajectory as shown in FIG. 10 containing the point of origin O.
When this frequency modulated wave is demodulated, the demodulated waveform shown in FIG. 3 will represent such a sine wave as shown in FIG. 6, as is the case with the above example, since the vector trajectory of the frequency modulated wave is determined by the instantaneous angular frequency. However, in the case of the demodulated wave as shown in FIG. 9, the demodulated waveform will take a large negative value at a position corresponding to the point P2 shown in FIG. 11 because the point P2 approaches the point of origin and the instantaneous angular frequency increases in a negative direction.
In the case of the demodulated waveform shown in FIG. 10, the vector trajectory encompasses the point of origin with the point P2 located close to the point of origin and, therefore, the instantaneous angular frequency takes a very large positive value. The consequence is that the demodulated waveform exhibits a very large positive value, so far from exhibiting a negative value which it ought to have taken, at the position corresponding to the point P2. This is called the reversal phenomenon in which the demodulated signal jumps towards the white level side.